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------------------------------------------------ Solve [tex]38.4 \ \textgreater \ \frac{x}{-3.3}[/tex]. Then graph the solution.

To solve the inequality [tex]\(38.4 > \frac{x}{-3.3}\)[/tex], follow these steps:

1. Understand the Inequality: We need to isolate [tex]\(x\)[/tex] on one side. Currently, [tex]\(x\)[/tex] is divided by [tex]\(-3.3\)[/tex].

2. Multiply Both Sides by [tex]\(-3.3\)[/tex]: To eliminate the division, multiply both sides of the inequality by [tex]\(-3.3\)[/tex]. Remember, whenever you multiply or divide by a negative number in an inequality, the inequality sign flips.

[tex]\[
38.4 \times (-3.3) < x
\][/tex]

3. Calculate the Multiplication: Perform the multiplication:

[tex]\[
38.4 \times (-3.3) = -126.72
\][/tex]

So, the inequality becomes:

[tex]\[
-126.72 < x
\][/tex]

4. Solution: The solution is [tex]\(x > -126.72\)[/tex]. This tells us that [tex]\(x\)[/tex] can be any number greater than [tex]\(-126.72\)[/tex].

5. Graphing the Solution:
- On a number line, draw an open circle at [tex]\(-126.72\)[/tex] to indicate that [tex]\(-126.72\)[/tex] is not included in the solution.
- Shade or draw an arrow to the right of [tex]\(-126.72\)[/tex] to represent all numbers greater than [tex]\(-126.72\)[/tex].

This visual indicates that any number to the right of [tex]\(-126.72\)[/tex] fulfills the condition [tex]\(x > -126.72\)[/tex].